Resistive switching devices such as memristors and chalcogenide phase change memory cells can be set to any of two or more different resistive states. Devices having two possible states can be set to either a low-resistance state, which typically corresponds with a binary “1”, “HI” or “on”, or a high-resistance state typically corresponding with a binary “0”, “LO” or “off”. Devices having more than two possible states are also coming into use. Resistive switching devices can serve as non-volatile memory cells that can be fabricated in nanoscale two-dimensional crossbar structures or other two-dimensional arrays in which each cell is connected between a row conductor and a column conductor with very high cell density. In such an array, a given storage cell may be accessed by selecting appropriate row and column conductors, for example by applying a voltage across the row conductor and the column conductor between which that given cell is connected.